Galileo and the Pendulum is a node for learning that is part of a rich cluster and course, The Galileo Project at Connexions. Other sections of the Galileo Project are his biography, family life, the Inquisition, and descriptions of his work on motion, mechanical devices, and the telescope.
Surely the great Galileo Galilei of 14th century Italy would gaze in pride on the achievements of his namesake, the Galileo spacecraft that explored the solar system from 1989-2003.
Kepler’s Laws, Newton’s formulas: grasping grand concepts from great teachers is the online luxury of this learn node. Rice University’s Galileo Project provides the Johannes Kepler biography. NASA spins in an overview for science teachers of Kepler’s Three Laws of Planetary Motion. The image with this post is from a Syracuse University Physics applet that animates Kepler’s Laws.
A class video lecture is provided of Ramamurti Shankar, the John Randolph Huffman Professor of Physics and Professor of Applied Physics at Yale. From from a course in the Fundamentals of Physics, the lecture on Kepler’s Laws covers these ideas: “The focus of the lecture is problems of gravitational interaction. The three laws of Kepler are stated and explained. Planetary motion is discussed in general, and how this motion applies to the planets moving around the Sun in particular.”
The first source in this learn node is an article the open access journal Public Library of Science Biology in which researchers explore how at the neural level we may sharpen what we see in the presence of eye movements. The journal’s December 2007 issue’s table of contents features the image shown to the left, with this explanation:
Our eyes are constantly moving, which blurs the image of the world across the retina. Shown here is a neural network model of the visual cortex that removes this motion blur by using neural connections that are matched to the statistics of eye movements. (see Pitkow et al., e331).
To learn more about where seeing occurs, Webvision has a discussion of “Roles of amacrince cells,” which are “cells of the vertebrate retina [which] are interneurons that interact at the second synaptic level of the vertically direct pathways consisting of the photoreceptor-bipolar-ganglion cell chain.” Just to take a peek at how the eye works, or to study in detail, the amacrince page is an excellent open resource created at the John Moran Eye Center, University of Utah: WEBVISION: The Organization of the Retnia and Visual System.
The University of Texas also has some outstanding online materials for learning about motion perception, including this page in a Center for Perceptual Systems. Even for beginning and young students, spending some time with webpages like these introduces basic ideas and tickles the curiosity about vision and the biology from which it arises.
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This learn node cluster math help available online virtually from an amazing array of open sources. The picture here of Wolfgang Pauli and Niels Bohr as they “stare in wonder at a spinning top” is from lectures by David Tong of Cambridge University on Classical Dynamics. The picture is included in the third Tong lecture titled The Motion of Rigid Bodies. Pauli and Bohr � great mathematicians of the early 20th century � would surely turn the full intensity of their wonder on how a click of a 21st century mouse sends students to math help, math problems and math mentors.
In a click or two this learn node crosses the Atlantic pond from Cambridge to MIT for Algebra I lectures or to a place to think about geometry themes and variations while listening to some Bach.
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